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The $C^*$-algebras of quantum lens and weighted projective spaces
Journal of Noncommutative Geometry, Volume: 12, Issue: 1, Pages: 195 - 215
Swansea University Author:
Tomasz Brzezinski
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DOI (Published version): 10.4171/JNCG/274
Abstract
It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of contin...
Published in: | Journal of Noncommutative Geometry |
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ISSN: | 1661-6952 |
Published: |
2018
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URI: | https://cronfa.swan.ac.uk/Record/cronfa37050 |
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2020-07-14T11:24:51.5454074 v2 37050 2017-11-24 The $C^*$-algebras of quantum lens and weighted projective spaces 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2017-11-24 SMA It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2n+1q and the cyclic group ℤN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(ℙnq(m0,…,mn)), interpreted as fixed points under the circle action on C(S2n+1q), are computed under a mild assumption on the weights. Journal Article Journal of Noncommutative Geometry 12 1 195 215 1661-6952 Quantum lens space; graph algebra 23 3 2018 2018-03-23 10.4171/JNCG/274 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-07-14T11:24:51.5454074 2017-11-24T13:07:51.9926568 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzeziński 1 Wojciech Szymański 2 Tomasz Brzezinski 0000-0001-6270-3439 3 0037050-24112017131039.pdf lens.pdf 2017-11-24T13:10:39.1530000 Output 387587 application/pdf Accepted Manuscript true 2017-11-24T00:00:00.0000000 true eng |
title |
The $C^*$-algebras of quantum lens and weighted projective spaces |
spellingShingle |
The $C^*$-algebras of quantum lens and weighted projective spaces Tomasz Brzezinski |
title_short |
The $C^*$-algebras of quantum lens and weighted projective spaces |
title_full |
The $C^*$-algebras of quantum lens and weighted projective spaces |
title_fullStr |
The $C^*$-algebras of quantum lens and weighted projective spaces |
title_full_unstemmed |
The $C^*$-algebras of quantum lens and weighted projective spaces |
title_sort |
The $C^*$-algebras of quantum lens and weighted projective spaces |
author_id_str_mv |
30466d840b59627325596fbbb2c82754 |
author_id_fullname_str_mv |
30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski |
author |
Tomasz Brzezinski |
author2 |
Tomasz Brzeziński Wojciech Szymański Tomasz Brzezinski |
format |
Journal article |
container_title |
Journal of Noncommutative Geometry |
container_volume |
12 |
container_issue |
1 |
container_start_page |
195 |
publishDate |
2018 |
institution |
Swansea University |
issn |
1661-6952 |
doi_str_mv |
10.4171/JNCG/274 |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
department_str |
School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
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description |
It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2n+1q and the cyclic group ℤN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(ℙnq(m0,…,mn)), interpreted as fixed points under the circle action on C(S2n+1q), are computed under a mild assumption on the weights. |
published_date |
2018-03-23T03:46:33Z |
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1763752220942139392 |
score |
11.021648 |